Question 1012045
I don't even think variation is a legitimate way to solve this problem but here's something.
Lets say each soldier eats 1 food unit every day. Forty days for 250 soldiers is 10,000 food units. After 10 days, they are down to 10,000-250*10=8,750. If there are now {{{250+50=300 soldiers}}}, they then subsequently will eat 300 food units a day. They will have food for {{{8750/300=29.16}}} days. If you must round, you'd round down, for 29 days.